Pixelated light cone near source with Eevee
OK, I've discovered the answer. 

In render setting for Eevee, go to 'Volumetrics' settings and change the 'tile size' to a smaller pixel size. You can also adjust the 'sample rate' settings underneath the 'tile size' settings.

This does seem to increase render time considerably however. 

Another simpler option is to widen the angle of you light cone. I don't know why, but this too seems to eliminate the problem. Perhaps someone else can expand on why.